A new family of estimators of the population variance  using information on population variance of auxiliary variable in sample surveys

Housila P.  Singh; Surya K.  Pal

doi:https://doi.org/10.59170/stattrans-2016-034

A new family of estimators of the population variance using information on population variance of auxiliary variable in sample surveys

Housila P. Singh School of Studies in Statistics, Vikram University, Ujjain-456010, M.P., India. , Surya K. Pal School of Studies in Statistics, Vikram University, Ujjain-456010, M.P., India. Statistics in Transition new series, vol. 17, 2016, 4, pages: 605-630 Published online: 1 December 2016 https://doi.org/10.59170/stattrans-2016-034

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ABSTRACT

This paper proposes a family of estimators of population variance S²_y of the study variable y in the presence of known population variance S²_x of the auxiliary variable x. It is identified that in addition to many, the recently proposed classes of estimators due to Sharma and Singh (2014) and Singh and Pal (2016) are members of the proposed family of estimators. Asymptotic expressions of bias and mean squared error (MSE) of the suggested family of estimators have been obtained. Asymptotic optimum estimator (AOE) in the family of estimators is identified. Some subclasses of estimators of the proposed family of estimators have been identified along with their properties. We have also given the theoretical comparisons among the estimators discussed in this paper.

KEYWORDS

Auxiliary variable, Study variable, Bias, Mean squared error, Efficiency comparison.

REFERENCES

CHANDRA, P., SINGH, H. P., (2001). Modified estimators for population variance that utilizes the kurtosis of an auxiliary variable in sample surveys. Vikram Math. Jour., 21, 31–36.

DAS, A. K., TRIPATHI, T. P., (1978). Use of auxiliary information in estimating the finite population variance. Sankhya, C, 40 (2), 139–148.

DIANA, G., GIARDAN, M., PERRI, P. F., (2011). An improved class of estimators for the population mean . Statist. Math. Appl., 20(2), 123–140.

GUPTA, S., SHABBIR, J., (2008). Variance estimation in simple random sampling using auxiliary information. Hacett. Jour. Math. Statist., 37 (1), 57–67.

HILAL, A. L., TAILOR, R., SINGH, H. P., VERMA, M. R., (2014). New alternatives to ratio estimators of population variance in sample surveys, Appl. Math. Comp., 247, 255–265.

ISAKI, C. T., (1983). Variance estimation using auxiliary information. Jour. Amer. Statist. Assoc., 78 (381), 117–123.

KADILAR, C., CINGI, H., (2005). A new ratio estimator in stratified random sampling. Commun. Statist. Theo. Meth., 34, 597–602.

KADILAR, C., CINGI, H., (2006). Ratio estimators for the population variance in simple and stratified random sampling. Appl. Math. Comp., 173 (2), 1047–1059.

KADILAR, C., CINGI, H., (2007). Improvement in variance estimation in simple random sampling. Commun. Statist. Theo. Meth., 36, 2075–2081.

KHAN, M., SHABBIR, J., (2013). A ratio type estimator for the estimation of population variance using quartiles of an auxiliary variable. Jour. Statist. Applica. Prob., 2 (3), 319–325.

LEE, K. H., (1981). Estimation of variance of mean using known coefficients of variation. Commun. Statist. Theo. Meth., A10 (5), 503–514.

PRASAD, B., SINGH, H. P., (1990). Some improved ratio-type estimators of finite population variance in sample surveys. Commun. Statist. Theo. Meth., 19 (3), 1127–1139.

PRASAD, B., SINGH, H. P., (1992). Unbiased estimators of finite population variance using auxiliary information in sample surveys. Commun. Statist. Theo. Meth., 21 (5), 1367–1376.

SEARLS, D. T., (1964). The utilization of a known coefficients variance in the estimation procedure. Jour. Amer. Statist. Assoc., 59 (308), 1225–1226.

SEARLS, D. T., INTARAPANICH, P., (1990). A note on an estimator for the variance that utilizes kurtosis. Amer. Statist., 44 (4), 295–296.

SEN, A. R., (1978). Estimation of the population mean when the coefficient of variation is known. Commun. Statist. Theo. Meth., A7 (7), 657–672.

SHABBIR, J., (2006). A new estimator of population mean in stratified sampling. Commun. Statist. Theo. Meth., 35 (7), 1201–1209.

SHABBIR, J., GUPTA, S., (2007). On improvement in variance estimation using auxiliary information. Commun. Statist. Theo. Meth., 36 (12), 2177–2185.

SHARMA, P., SINGH, R., (2014). Improved dual to variance ratio type estimators for population variance. Chilean Jour. Statist., 5 (2), 45–54.

SINGH, H. P., PAL, S. K., SOLANKI, R. S., (2013). Improved estimation of finite population variance using quartiles. Istatistik- Jour. Tur. Stat. Assoc., 6 (3), 166–121.

SINGH, H. P., PAL, S. K., SOLANKI, R. S., (2014). A new procedure for estimation of finite population variance using auxiliary information. Jour. Reliab. Stat. Stud., 7 (2), 149–160.

SINGH, H. P., AGNIHOTRI, N., (2008). A general procedure of estimating population mean using auxiliary information in sample surveys. Statist. Trans. new series, 9 (1), 71–78.

SINGH, H. P., PAL, S. K., (2016). An efficient class of estimators of finite population variance using quartiles. Jour. Appl. Stat., 43 (10), 1945–1958.

SINGH, H. P., SOLANKI, R. S., (2013a). A new procedure for variance estimation in simple random sampling using auxiliary information. Statistical Papers, 54 (2), 479–497.

SINGH, H. P., SOLANKI, R. S., (2013b). Improved estimation of finite population variance using auxiliary information. Commun. Statist. Theo. Meth., 2 (15), 2718–2730.

SINGH, H. P., (1986). A note on the estimation of variance of sample mean using the knowledge of coefficients of variation in natural population. Commun. Statist. Theo. Meth., 15 (12), 3737–3746.

SINGH, H. P., UPADHYAYA, L. N., NAMJOSHI, U. D., (1988). Estimation of finite population variance. Cur. Sci., 57 (24), 1331–1334.

SINGH, J., PANDEY, B. N., HIRANO, K., (1973). On the utilization of a known coefficient of kurtosis in estimation procedure of variance. Amn. Inst. Statist. Math., 25 (1), 51–55.

SINGH, R., MALIK S., (2014). Improved estimation of population variance using information on auxiliary attribute in simple random sampling. Appl. Math. Comp., 235, 43–49.

SOLANKI, R. S., SINGH, H. P., (2013). An improved class of estimators for the population variance. Mod. Assist. Statist. Appl., 8 (3), 229–238.

SOLANKI, R. S., SINGH, H. P., PAL, S. K., (2015). Improved ratio-type estimators of finite population variance using quartiles, Hacettepe Jour. Math. Stat., 44 (3), 747–754.

SRIVASTAVA, S. K., JHAJJ, H. S., (1980). A class of estimators using auxiliary information for estimating finite population variance. Sankhya, C, 42 (1-2), 87–96.

SUBRAMANI, J., KUMARAPANDIYAN, G., (2012a). Variance estimation using median of the auxiliary variable. Inter. Jour. Prob. Statist., 1 (3), 62–66.

SUBRAMANI, J., KUMARAPANDIYAN, G., (2012b). Variance estimation using quartiles and their functions of an auxiliary variable. Inter. Jour. Statist. Appl., 2 (5), 67–72.

UPADHYAYA, L. N., SINGH, H. P., (1984): On the estimation of the population mean with known coefficient of variation. Biometrical Jour., 26 (6), 915–922.

UPADHYAYA, L. N., SINGH, H. P., (1986). On a dual to ratio estimator for estimating finite population variance. Nepal Math. Sci. Rep., 11 (1), 37–42.

UPADHYAYA, L. N., SINGH, H. P., (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical Jour., 41 (5), 627–636.

YADAV, S. K., PANDEY, H., (2012). Improved family of estimators for the population variance using qualitative auxiliary information. Assam Statist. Rev., 26 (2), 63–70.

YADAV, S. K., KADILAR, C., SHABBIR, J., GUPTA, S., (2015). Improved family of estimators of population variance in simple random sampling. Jour. Statist. Theo. Pract., 9, 219–226.